Before starting, I think in some cases it is normal not to be able to find 100% correct/equivalent translation between languages.
"What if we don't call him" means: "onu çağırmazsak ne olur/ ya onu çağırmazsak?"
for more proper (but (definitely) not equivalent) meaning I recommend one of these:
"should/could we call also him?"
"what if we call also him?" (negation is not required)
"will/shall we call also him?"
meanwhile, the response to these expressions can be one of these:
"a evet,iyi fikir" (oh yes, that is good idea)
"çağıralım,neden olmasın" (yes we call him, why not)
"problem değil o da gelsin/gelebilir" (no problem he also can come)